Möbius Transformation and Einsten Velocity Addition in the Hyperbolic Geometry of Bolyai and Lobachevsky
arXiv:1303.4785
Abstract
In this chapter, dedicated to the 60th Anniversary of Themistocles M. Rassias, Möbius transformation and Einstein velocity addition meet in the hyperbolic geometry of Bolyai and Lobachevsky. It turns out that Möbius addition that is extracted from Möbius transformation of the complex disc and Einstein addition from his special theory of relativity are isomorphic in the sense of gyrovector spaces.
arXiv admin note: substantial text overlap with arXiv:1302.6961